Implementation using FFT

Dear,

See the following image, may help you:

Thank you so much Sir for your help.

But I am applying this algorithm to an input signal BFSK that have as frequency 868 Mhz and I am using as sampling frequency 2048 Hz for the algorithm.are those values related to each other ??

because as far as I read the frequency of sampling is the frequency of extracting the samples from the input signal but when I look to the picture that you have attached I see that alpha and f should be in the range of [-Fs/2,Fs/2].

what do you think please ?

Hi Jaoua. The sampling frequency fs must be at least as large as twice the largest frequency (at least classically!) in your signal. The spectrum of BFSK has two sidebands, one centred on the lower frequency applied and one on the higher frequency applied. These are usually centred equally around a frequency fc (so that f_lower = fc-DeltaF, f_higher = fc + DeltaF) (forgive the notation!). The spectrum will be spread around these values according to a sinc function due to the pulsed nature of the modulation applied.

So putting it all together, a BFSK is defined by two frequencies, or one frequency and a spacing. Your sample frequency fs must be at least twice the higher frequency plus a bit to allow for spreading (related to the pulsing duration).

I couldn't see in the paper where those numbers came from, but if I can assume fc is 868MHz then fs of 2048MHz would assume that the f_higher is no greater than 1024MHz, a spacing of 156MHz from fc. Does this stack up with your observations?